##
#  Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
#
#  File :      lo1.py
#
#  Purpose :   Demonstrates how to solve small linear
#              optimization problem using the MOSEK Python API.
##
import sys
import mosek

# Since the value of infinity is ignored, we define it solely
# for symbolic purposes
inf = 0.0

# Define a stream printer to grab output from MOSEK
def streamprinter(text):
    sys.stdout.write(text)
    sys.stdout.flush()


def main():
    # Create a task object
    with mosek.Task() as task:
        # Attach a log stream printer to the task
        task.set_Stream(mosek.streamtype.log, streamprinter)

        # Bound keys for constraints
        bkc = [mosek.boundkey.fx,
               mosek.boundkey.lo,
               mosek.boundkey.up]

        # Bound values for constraints
        blc = [30.0, 15.0, -inf]
        buc = [30.0, +inf, 25.0]

        # Bound keys for variables
        bkx = [mosek.boundkey.lo,
               mosek.boundkey.ra,
               mosek.boundkey.lo,
               mosek.boundkey.lo]

        # Bound values for variables
        blx = [0.0, 0.0, 0.0, 0.0]
        bux = [+inf, 10.0, +inf, +inf]

        # Objective coefficients
        c = [3.0, 1.0, 5.0, 1.0]

        # Below is the sparse representation of the A
        # matrix stored by column.
        asub = [[0, 1],
                [0, 1, 2],
                [0, 1],
                [1, 2]]
        aval = [[3.0, 2.0],
                [1.0, 1.0, 2.0],
                [2.0, 3.0],
                [1.0, 3.0]]

        numvar = len(bkx)
        numcon = len(bkc)

        # Append 'numcon' empty constraints.
        # The constraints will initially have no bounds.
        task.appendcons(numcon)

        # Append 'numvar' variables.
        # The variables will initially be fixed at zero (x=0).
        task.appendvars(numvar)

        for j in range(numvar):
            # Set the linear term c_j in the objective.
            task.putcj(j, c[j])

            # Set the bounds on variable j
            # blx[j] <= x_j <= bux[j]
            task.putvarbound(j, bkx[j], blx[j], bux[j])

            # Input column j of A
            task.putacol(j,                  # Variable (column) index.
                         asub[j],            # Row index of non-zeros in column j.
                         aval[j])            # Non-zero Values of column j.

        # Set the bounds on constraints.
         # blc[i] <= constraint_i <= buc[i]
        for i in range(numcon):
            task.putconbound(i, bkc[i], blc[i], buc[i])

        # Input the objective sense (minimize/maximize)
        task.putobjsense(mosek.objsense.maximize)

        # Solve the problem
        task.optimize()
        # Print a summary containing information
        # about the solution for debugging purposes
        task.solutionsummary(mosek.streamtype.msg)

        # Get status information about the solution
        solsta = task.getsolsta(mosek.soltype.bas)

        if (solsta == mosek.solsta.optimal):
            xx = task.getxx(mosek.soltype.bas)
            
            print("Optimal solution: ")
            for i in range(numvar):
                print("x[" + str(i) + "]=" + str(xx[i]))
        elif (solsta == mosek.solsta.dual_infeas_cer or
              solsta == mosek.solsta.prim_infeas_cer):
            print("Primal or dual infeasibility certificate found.\n")
        elif solsta == mosek.solsta.unknown:
            print("Unknown solution status")
        else:
            print("Other solution status")


# call the main function
try:
    main()
except mosek.Error as e:
    print("ERROR: %s" % str(e.errno))
    if e.msg is not None:
        print("\t%s" % e.msg)
        sys.exit(1)
except:
    import traceback
    traceback.print_exc()
    sys.exit(1)